Implementation of various-fidelity methods for viscous effects modeling on the design of a waverider

Abstract

In the present study, the implementation of three viscous effects modeling methods at hypersonic flow conditions is investigated. The design of a hypersonic passenger transport waverider configuration is employed as a case study. The methods, each of which has a different fidelity level, are evaluated in terms of their capability to predict aerodynamic performance, as well as their effect on the final geometric design of the waverider. More specifically, for the same mission profile and design constraints, three different waverider configurations (Cases A, B and C) are designed with the osculating cone methodology, and each employing a different viscous effect modeling method. These three configurations are designed (a) assuming a purely inviscid flowfield, (b) using Eckert's Reference Temperature and (c) Van Driest's viscous effects modeling semi-empirical methods respectively, each subsequent one of higher complexity and fidelity than the previous. An optimization loop, employing the Nelder-Mead simplex algorithm, is also incorporated into the overall design process. Each configuration is evaluated with all three viscous effects modeling methods and the analytical results are compared against those of CFD modeling. The CFD analyses are performed by solving the steady-state three-dimensional Euler and Reynolds Averaged Navier Stokes (RANS) equations. Overall, the three configurations are evaluated in terms of aerodynamic performance, design/optimization computational cost, and accuracy between the analytical and CFD results. All inviscid analytical calculations demonstrate very good agreement with the Euler CFD results. Indicatively, the lift-to-drag predictions deviate by as much as 2% between the two approached. The Van Driest's method predictions result to 5%-6.5% lower lift-to-drag ratios compared to the RANS CFD, and to higher wall shear stress values. Contrarily, the Ref. Temperature method predictions are in a much closer agreement to the RANS CFD results, leading to a slight overprediction (0%-2.4%) of lift-to-drag ratios. The incorporation of viscous effects in the design process reduces the waverider's aerodynamic efficiency by about 8.5%-11% and results in a 46%-98% increase in computational time, compared to the inviscid analysis.